An elevator's cable can handle a tension of 95,500N. Assuming the car has a mass of 2950 kg and it is carrying a full load of passengers whose combined mass is 3750 kg, what is the minimum time required for the elevator to rise 50.0 m from rest?

95500=m(g+a)

solve for a.

Now, you can use a to figure time up...
vf^2=2ad solve for vf, then vavg=vf/2, and time up=50/Vavg

However, in the real world, elevators do no have constant acceleration as they travel. The accelerate to a fixed set max velocity, then travel at that velocity. Think of the difficulty of a constantly accelerating elevator...such as stopping it at floor 100...

To find the minimum time required for the elevator to rise 50.0 m from rest, we first need to calculate the tension in the elevator's cable when it is carrying the car and the passengers.

The total mass being lifted by the elevator is the sum of the mass of the car and the mass of the passengers:

Total mass = mass of car + mass of passengers
= 2950 kg + 3750 kg
= 6700 kg

Since the elevator is accelerating upwards, there will be a net force acting on the elevator equal to the tension in the cable, which is the force pulling the elevator up, minus the force due to gravity pulling the elevator down.

The force pulling the elevator up is equal to the tension in the cable, and the force due to gravity pulling the elevator down is equal to the weight of the elevator.

Weight = mass * acceleration due to gravity
= total mass * g
= 6700 kg * 9.8 m/s^2
= 65660 N

Now we can calculate the tension in the cable:

Tension = force pulling the elevator up + force due to gravity
= T + Weight
= T + 65660 N

Since we are given that the cable can handle a tension of 95,500 N, we can set up the following equation:

T + 65660 N = 95500 N

Solving for T:

T = 95500 N - 65660 N
= 29840 N

Now that we have the tension in the cable, we can calculate the acceleration of the elevator using Newton's second law:

Net force = mass * acceleration
29840 N = 6700 kg * acceleration

Solving for acceleration:

acceleration = 29840 N / 6700 kg
≈ 4.457 m/s^2

Finally, we can find the minimum time required for the elevator to rise 50.0 m from rest using the equation of motion:

Δy = v0 * t + (1/2) * a * t^2

where Δy is the displacement (50.0 m in this case), v0 is the initial velocity (0 m/s since the elevator starts from rest), t is the time, and a is the acceleration.

Plugging in the values:

50.0 m = 0 * t + (1/2) * 4.457 m/s^2 * t^2

Rearranging and solving for t:

25.0 m = 2.2285 m/s^2 * t^2

t^2 = 25.0 m / 2.2285 m/s^2
t^2 ≈ 11.208 s^2

t ≈ √(11.208 s^2)
t ≈ 3.347 s

Therefore, the minimum time required for the elevator to rise 50.0 m from rest is approximately 3.347 seconds.